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Volume 4, Issue 4
On Time-Space Fractional Reaction-Diffusion Equations with Nonlocal Initial Conditions

Pengyu Chen & Peng Gao

DOI: 10.12150/jnma.2022.791

J. Nonl. Mod. Anal., 4 (2022), pp. 791-807.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of mild solution to the reaction-diffusion equation are obtained by solving the abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. The results in this paper improve and extend some related conclusions to this topic.

  • Keywords

Time-space fractional reaction-diffusion equation, Nonlocal initial condition, Mild solution, Existence and uniqueness, Mittag-Leffler-Ulam stability.

  • AMS Subject Headings

35R11, 47J35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-791, author = {Chen , Pengyu and Gao , Peng}, title = {On Time-Space Fractional Reaction-Diffusion Equations with Nonlocal Initial Conditions}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {791--807}, abstract = {

This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of mild solution to the reaction-diffusion equation are obtained by solving the abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. The results in this paper improve and extend some related conclusions to this topic.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.791}, url = {http://global-sci.org/intro/article_detail/jnma/21913.html} }
TY - JOUR T1 - On Time-Space Fractional Reaction-Diffusion Equations with Nonlocal Initial Conditions AU - Chen , Pengyu AU - Gao , Peng JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 791 EP - 807 PY - 2023 DA - 2023/08 SN - 4 DO - http://doi.org/10.12150/jnma.2022.791 UR - https://global-sci.org/intro/article_detail/jnma/21913.html KW - Time-space fractional reaction-diffusion equation, Nonlocal initial condition, Mild solution, Existence and uniqueness, Mittag-Leffler-Ulam stability. AB -

This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of mild solution to the reaction-diffusion equation are obtained by solving the abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. The results in this paper improve and extend some related conclusions to this topic.

Pengyu Chen & Peng Gao. (2023). On Time-Space Fractional Reaction-Diffusion Equations with Nonlocal Initial Conditions. Journal of Nonlinear Modeling and Analysis. 4 (4). 791-807. doi:10.12150/jnma.2022.791
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